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Asymptotic bounds for the expected L1 error of a multivariate kernel density estimator

Author

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  • Holmström, Lasse
  • Klemelä, Jussi

Abstract

The kernel estimator of a multivariate probability density function is studied. An asymptotic upper bound for the expected L1 error of the estimator is derived. An asymptotic lower bound result and a formula for the exact asymptotic error are also given. The goodness of the smoothing parameter value derived by minimizing an explicit upper bound is examined in numerical simulations that consist of two different experiments. First, the L1 error is estimated using numerical integration and, second, the effect of the choice of the smoothing parameter in discrimination tasks is studied.

Suggested Citation

  • Holmström, Lasse & Klemelä, Jussi, 1992. "Asymptotic bounds for the expected L1 error of a multivariate kernel density estimator," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 245-266, August.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:2:p:245-266
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    Citations

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    Cited by:

    1. Gordon Anderson & Oliver Linton & Yoon-Jae Wang, 2009. "Non Parametric Estimation of a Polarization Measure," Working Papers tecipa-363, University of Toronto, Department of Economics.
    2. Nussbaum, Michael & Klemelä, Jussi, 1998. "Constructive asymptotic equivalence of density estimation and Gaussian white noise," SFB 373 Discussion Papers 1998,53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    4. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.

    More about this item

    Keywords

    nonparametric density estimation multivariate kernel estimator L1 error discrimination numerical simulations;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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